Co-Investigators John W White, Philip A Reynolds and Piotr A
Wielopolski

Research School of Chemistry and

Australian National University Supercomputer Facility

Molecular Simulations of Superconducting Crystals RbxC60

Reaction of buckminsterfullerene, C60, with alkali metals can result in
materials which remain superconducting to high temperatures (e.g. Rb3C60 Tc=
30K). Other compositions, alkali metals, and dopings of other molecules,
change the electrical properties markedly. Our recent work has concentrated on
linking the structure and dynamics of some of these materials to their
superconductivity [1,2]. It has become clear that while the interaction of the
potentially superconducting electrons with vibrations of the C60 ball is
important, details of the structure are equally so. X-ray and neutron
experiments show that the time-average of the structures are mostly disordered.
Molecular simulation of the crystal structures offers a way of examining the
time development of the structures which is not available experimentally. In
particular we will attempt to simulate the relative positions and hopping
motions of the rubidiums relative to the C60 balls, and the resulting charge
changes on the balls themselves. Understanding this may provide clues about
the mechanism of superconductivity in this class of materials.

What are the basic questions addressed?

Superconductivity in the RbxC60 system requires electron transport between C60
balls. Experimentally this is modified by rubidium content. We wish to know
the arrangement of the rubidiums within the crystal, and the effect this
arrangement has on the electron distribution on the C60 fragments, for varying
rubidium contents. This information is not available experimentally. As a
first approximation we will use a classical model which has been used
successfully in the graphite intercalates.

What are the results to date and the future of the work?

Before we did any computation we imagined that the rubidiums would not
be very ordered, and that they would move among the holes between the C60's in
a somewhat random fashion, only correlating their motion sufficiently to
prevent Rb-Rb overlap. We conceived of the charge on the C60 balls as merely
modifying this by providing screening, even if this was quite large. That is
to say the behaviour would resemble the Cs-graphite simulations.

The first simulations (of RbC60) showed very different behaviour. Realistic
Rb+-Rb+ potentials and electrostatic forces produced a
very ordered tetragonal structure. So ordered that it is difficult to
reconcile with the (alleged) cubic time-average experimental structure. Each
C60 seemed to interact with a single Rb+, producing a highly
polarised RbC60 `dimer'. These `dimers' then become mutually orientationally
order.ed -- there was no hopping and no appreciable disorder.

Further simulations showed that this conclusion was hardly dependent on the
strength of the interactions. Changes of about a factor of ten in potentials
change the structure little.

The departure of the principal investigator from ANU has slowed the pace of
work, but it is now clear that there is an unexplained discrepancy between
theory and experiment. Further investigation of starting configurations,
boundary conditions, charge and potential models are required before we can
definitively state that our understanding of the physically important factors
here requires change.

What computational techniques are used and why is a supercomputer
required?

We calculate the equilibrium molecular dynamics in an isokinetic
canonical ensemble (N,V,T). The equation of motion is solved using a
fourth-order predictor-corrector Gear scheme, and energy minimisation by a
multidimensional steepest gradient method. Because of the large scope for
vectorisation of the code in the most time-consuming routines (force
calculations, energy minimisation) the VP2200 is ideal for this type of
calculation.

The simulations require the numerical solution of the equations of motion of
128 or 256 rubidium ions in a fixed body centred tetragonal framework of C60
ions. Each C60 has a charge fixed so as to make the whole crystal
electroneutral. This charge is confined to the surface of the C60 ball, but
otherwise is free to respond to the motion of the Rb+ ions. The
solution of this problem is computationally demanding because of the large
number of long-range charge-charge interactions, and because of the need to
iterativelydue to the release of pressure solve detailed charge distributions
and energies at a given rubidium distribution.